TOMS424
Clenshaw-Curtis Integration

TOMS424 is a FORTRAN77 library which implements ACM TOMS algorithm 424, for Clenshaw-Curtis quadrature to estimate the integral of a function F(X) from A to B.

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, most of the early algorithms are not available. This is one of them. I typed it in.

Usage:

quad = CCQUAD(F,A,B,TOLERR,LIMIT,ESTERR,USED,CSXFRM)

returns an estimate of the integral of F(X) from A to B, with the requested relative accuracy TOLERR, using no more than LIMIT function evaluations, achieving an estimated error of ESTERR, and actually using USED function evaluations. The cosine tranform is returned in CSXFRM(1:USED).

Languages:

TOMS424 is available in a FORTRAN77 version.

Related Programs:

INTLIB, a FORTRAN90 library which estimates integrals.

TEST_INT, a FORTRAN90 library which defines many test integrands.

Reference:

1. Charles Clenshaw, Alan Curtis,
   A Method for Numerical Integration on Automatic Computers,
   Numerische Mathematik,
   Volume 2, Number 1, December 1960, pages 197-205.
2. W Morven Gentleman,
   Algorithm 424: Clenshaw-Curtis Quadrature,
   Communications of the ACM,
   Volume 15, Number 5, May 1972, pages 353-355.

Source Code:

• toms424.f, the source code.
• toms424.sh, commands to compile the source code.

Examples and Tests:

• toms424_prb.f, a sample calling program.
• toms424_prb.sh, commands to compile and run the sample program.
• toms424_prb_output.txt, the output file.

List of Routines:

• CCQUAD is the routine called by a user to estimate the integral of a function F(X) from A to B, using Clenshaw-Curtis quadrature.
• R3PASS carries out a radix 3 pass of a Fast Fourier Transform.

You can go up one level to the FORTRAN77 source codes.